1. Field of the Invention
The present invention relates to a linear guide way with parabolic profiled grooves, and more particularly, to a linear guide way whose cross sectional profiles of both railway and slider grooves are configurated into a parabola so as to acquire an optimistic contact between balls and grooves.
2. Description of the Prior Art
A linear guide way is an important mechanism which has been widely employed as one of the mechanical components in the precision machines, the automation industry, the semiconductor industry, the medical application and the aerospace technology. The smooth motion of this mechanism relies on a plurality of balls rolling in the grooves of the guide way so as to reduce the frictional and heat losses arising on the contact surface of the slider and the rail way thereby speeding up the motion of the mechanism and, at the same time, improving its durability.
FIG. 6 is a perspective view of a conventional linear guide way. The linear guide way includes a rail way 1, a slider 2, and a plurality of balls. The rail-way 1 has a rail-way groove 11 provided in the lengthwise direction of the rail-way 1. The slider 2 provided with a slider groove 21 at the position corresponding to the rail-way groove 11, is set on the rail-way 1. The balls 3 are sandwiched between the rail-way groove 11 and the slider groove 21 to assist the slider 2 to travel along the lengthwise direction with their rolling motion in the two grooves 11 and 21. For convenience, the two grooves 11 and 21 will be collaborated in one to call the “rolling groove” hereinafter. Circulation holes 22 formed on the slider 2 provide a return passage for the balls 3 such that they are able to circulate by way of the rolling groove and the circulation holes 22.
FIG. 7 is a schematic view showing the cross section of a conventional rolling grove. As shown in FIG. 7, the pure arc AB is the cross section profile line of the rail-way groove 11 or the slider groove 21, wherein the point A and point B is the two end points of the arc AB. It can be clearly seen that the radius of arc AB is slightly larger than that of the circle O, which is the projection of the ball 3. The center of the arc AB is O', and point T is the contact point between the curve (arc) AB and the circle O. Line OT connects O and T. By connecting the center O and an arbitrary point C on the arc AB, the line OC intersects the circle O at point D forming angle θ between OC and OT, where the length of OD equals to the radius of circle O.
Here, define the radius of circle O as R, it is also the radius of the ball 3, and define the distance O'O as Δ, which is also the difference between the radius of arc AB and that of circle O, then O'C equals to the radius of arc AB, that is (Δ+R). Line CD represent the clearance formed between the ball 3 and the rolling groove. Here let us put CD=δ, according to the principle of geometry, θ,δ,R and Δ have the relation asδ/R=√{square root over ( )}(Δ2 COS2θ+2Δ+1)−Δ cosθ−1.
Since factor δ/R is a nondimensional value which has nothing to do with the dimension of length. Besides, for convenience, define
η=radius of arc AB/diameter of circle O, where η is called coefficient of figure. It is also dimensionless and can be expressed by the following formula:η=(1+Δ/R)/2
The relationship of various η with respect to the angle θ is expressed in the graphs of FIG. 8. As shown in FIG. 8, values of θ are expressed on the X axis while values of S/R are on the Y axis, where δ/R is a nondimensional ratio, Referring to the left curve of FIG. 8, where η=0.56, then S/R=10−4, we get θ≈2.5° on the graph. If η=0.51, then δ/R=10−4, we get θ≈6°. But when η<0.5, then values δ/R are all nil that means there is a full contact between arc AB and circle O.
According to the international standards, a significant permanent non-restorable (destructive) deformation is considered to happen to a ball when its deformation reaches the value 10−4 of its diameter. Of course, in the general case, the deformation of a ball is never allowed to approach the value 10−4 of its diameter. As shown in FIG. 8, assume η=0.56, when δ/R≦10−4, θ≦2.5°, this is a very small value that means the region of permissible load for a ball is very strictly limited. In order to liberate this limit effectively, lowering the value of η is a feasible consideration. If η=0.53, θ can be enlarged to 3.4°; if η=0.52, θ is further enlarged to 4°; if η=0.51, θ reaches 6°. Form now on, if η is recklessly to 0.5 erroneously, δ/R becomes nil and the arc AB fully contacts the circle O which brings the ball to make a flat contact with the grooves resulting in a serious friction or even destructive abrasion therebetween.
Incidentally, an inevitable minor fabrication error results in a slight deviation in sizes of ball, or arc radius of rolling groove. A larger η causes degrading the loading ability of the linear guide way, on the other hand, if η approaches 0.5, an undesirable danger of severe abrasion to the mechanism of the linear guide way is likely to happen.
In order to avoid falling into such a dilemmatic state when fabricating a linear guide way, a practical improvement in designing a rolling groove having an optimistic profile to eliminate the inherent disadvantages described above is definitely necessary.